A method to approximate transmission probabilities for a nonseparable multidimensional barrier is applied to a waveguide model. The method uses complex barrier-crossing orbits to represent reaction probabilities in phase space and is uniform in the sense that it applies at and above a threshold energy at which classical reaction switches on. Above this threshold the geometry of the classically reacting region of phase space is clearly reflected in the quantum representation. Two versions of the approximation are applied. A harmonic version which uses dynamics linearized around an instanton orbit is valid only near threshold but is easy to use. A more accurate and more widely applicable version using nonlinear dynamics is also described.A method to approximate transmission probabilities for a nonseparable multidimensional barrier is applied to a waveguide model. The method uses complex barrier-crossing orbits to represent reaction probabilities in phase space and is uniform in the sense that it applies at and above a threshold energy at which classical reaction switches on. Above this threshold the geometry of the classically reacting region of phase space is clearly reflected in the quantum representation. Two versions of the approximation are applied. A harmonic version which uses dynamics linearized around an instanton orbit is valid only near threshold but is easy to use. A more accurate and more widely applicable version using nonlinear dynamics is also described.

arXiv:nlin/0506009Physical Review ADec 1, 200515 citations

BARRIER PENETRATION: SEMI-CLASSICAL APPROXIMATION

Jean Zinn‐Justin

Oxford University Press eBooksNov 18, 20040 citations

Polarization effects in penetration of a barrier with a magnetic field applied

J. Schmit, Robert H. Good

The spin polarization of an electron moving nonrelativistically through a potential barrier $V(z)$ , with also a constant uniform magnetic field ( $0,0,B$ ) applied, is calculated using the WKB approximation for the $z$ dependence of the wave function. It is found that, in a classically allowed region, the polarization precesses at fixed angle $\ensuremath{\theta}$ about the magnetic field, with phase angle the same as a classical particle with a magnetic dipole moment. The particle penetrates through the barrier with no change in the phase of the precession but with a discontinuity in $\ensuremath{\theta}$.The spin polarization of an electron moving nonrelativistically through a potential barrier $V(z)$, with also a constant uniform magnetic field ($0,0,B$) applied, is calculated using the WKB approximation for the $z$ dependence of the wave function. It is found that, in a classically allowed region, the polarization precesses at fixed angle $\ensuremath{\theta}$ about the magnetic field, with phase angle the same as a classical particle with a magnetic dipole moment. The particle penetrates through the barrier with no change in the phase of the precession but with a discontinuity in $\ensuremath{\theta}$.

Physical review. B, Solid stateAug 1, 19774 citations

The spin polarization of an electron moving nonrelativistically through a potential barrier

V(z)

, with also a constant uniform magnetic field (

0,0,B

) applied, is calculated using the WKB approximation for the

z

dependence of the wave function. It is found that, in a classically allowed region, the polarization precesses at fixed angle $\ensuremath{\theta}$ about the magnetic field, with phase angle the same as a classical particle with a magnetic dipole moment. The particle penetrates through the barrier with no change in the phase of the precession but with a discontinuity in $\ensuremath{\theta}$.